How can I light up a dark scene correctly in Cycles, so it looks as in a dark room with only one light (as a lamp, for example)
"Correct lighting" is highly subjective, and so my answer is just based on my personal preferences and not some formula of doing things 'right'.
To start, I like to use at least a bit of ambient occlusion or global illumination on the scene to prevent large areas of the scene to be lost in shadow. In general you should try to avoid absolute black values.
Add a point lamp wherever your light source would be in the scene or if you have a lightbulb mesh, you could add an emission material to it for more accuracy. Then simply play around with the lamp/emission settings until you get a level of brightness you like. Try turning off AO to see the effect of only your light. Also note that you can enter a negative value into a lamp object and place it in corners of the scene that you want to look extra dark.
Hope that gives you an idea or two.
This video shows how to set up an object (in this case a plane) as an emmitter of light. In your case you could use a Sphere instead, and play around with the size of the sphere to get the right feel. (this will help prevent extremely sharp shadows)
The video also shows how to hide the emitting object from the view of the render camera. (It still "works", but the object itself is invisible).